Semiempirical molecular orbital calculations with linear system size scaling

Details are provided for the implementation of a density matrix divide-and-conquer approximation into the framework of molecular orbital theory on nonperiodic systems. Originally developed for density functional theory, the divide-and-conquer procedure is one of the most promising in a growing list of techniques that exhibit linear scaling with respect to the number of basis functions in the system. The key to linear scaling is the division of the electronic structure calculation into a series of calculations over a set of small, overlapping subsystems. A semiempirical molecular orbital program designed around the divide-and-conquer approach has been written and a number of tests are carried out on polyglycine structures in order to evaluate its performance. For the systems examined, linear scaling is indeed observed, and the accuracy of the calculations can be controlled quite readily by the manner in which the system is divided into its component subsystems. For very large structures, the expense associated with the computation of two-center interactions will ultimately dominate the calculation, and quadratic scaling will become apparent. Techniques to linearize this aspect of the calculation are investigated and discussed.